161.

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Figure 6.6 (a) Hierarchical model showing a region pattern at the higher level, while the texture patterns apply at lower level, (b) High level is replaced by a user-defined region image, which is then filled texture at low level with β=(2, 2, 2, 2) (in the white region), (−1, 2, − 1, 2) (in the grey region), and (− 1, −1, − 1,−1) (in the black region).

6.2.1 Posterior energy for image classification

Using Bayesian formulae, the posterior distribution P(w_r|d_r) for label w_r given the observation d_r at pixel r is correlated with P(d_r|w_r)P(w_r) (Chapter 2). According to Equation (6.1), P(w_r)=(1/Z)·exp[−U(w_r)], and the U(w_r) is therefore called the prior energy. Here, we use a smoothness assumption as prior information. If only cliques C₁ and C₂ are included in a MLL model (Section 6.1.4) then the prior energy (smoothness prior) for pixel r can be defined as:

(6.14)

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